Data-driven projections such as those proposed in
[1]}, [2]}, [3]}, [4]}
can keep the increased noise level at bay,
by effectively working under the sparsity assumption on \(\mathbf {d}_j\) 
and consequently considering only a subset of all possible projections.
This comes at the cost of decreased high-dimensional efficiency
when the sparsity assumption is not met,
compared to the oracle projection with respect to \(\mathbf {p}_{\text{o}}\) 
or the \(\ell _2\) -norm minimax optimal procedures such as [5]}, [6]}.
